A Geometric Design Method for Side-Stream Distillation Columns †

A Geometric Design Method for Side-Stream Distillation Columns†

Raymond E. Rooks, Michael F. Malone,* and Michael F. Doherty

Department of Chemical Engineering, University of Massachusetts, Amherst, Massachusetts 01003-3110

A side-stream distillation column may replace two simple columns for some applications,sometimes at considerable savings in energy and investment. This paper describes a geometricmethod for the design of side-stream columns; the method provides rapid estimates of equipmentsize and utility requirements. Unlike previous approaches, the geometric method is applicableto nonideal and azeotropic mixtures. Several example problems for both ideal and nonidealmixtures, including azeotropic mixtures containing distillation boundaries, are given. We makeuse of the fact that azeotropes or pure components whose classification in the residue curvemap is a saddle can be removed as side-stream products. Significant process simplificationsare found among some alternatives in example problems, leading to flow sheets with fewer unitsand a substantial savings in vapor rate.

Introduction and Background

Side-stream columns (Figure 1) offer an alternativeto sequences of simpler two-product columns. Intu-itively, the side stream should contain primarily middle-boiling components from a multicomponent mixture.Side streams may be useful when the middle boilers aretrace components or even the main product, as in apasteurization column where the lighter trace compo-nents leave overhead. The control of a side-streamcolumn may also need study, but that is not the topicof this paper. Instead, we consider a more primitivequestion, namely, “which side-stream columns offer asignificant economic advantage”, e.g., large enough tojustify the control study.Design methods for side-stream columns separating

mixtures with vapor-liquid equilibrium (VLE) charac-terized by a constant volatility model are available forboth single-feed (Glinos and Malone, 1985a) and double-feed (Nikolaides and Malone, 1987) configurations.These design methods were developed for “sharp splits”where the major products are essentially free of at leastone of the components in the feed. The question offeasibility for side-stream columns has not been ad-dressed in any detail, probably because the behavior ofideal mixtures is intuitive, i.e., intermediate-boilingcomponents will appear in the side stream, while thelightest and heaviest components concentrate as distil-late and bottoms, respectively.Criteria for use of side streams for the separation of

mixtures that do not exhibit azeotropes were firstdeveloped by Tedder and Rudd in 1978. They analyzedseveral column configurations, including side-streamcolumns, and developed criteria for their use in termsof an ease of separation index (ESI), which is a ratio ofthe relative volatilities (presumably constant or average)of the various components. The results suggest takinga vapor as a side-stream product if the side stream isbelow the feed and a liquid side-stream product if theside stream is above the feed.An important result from earlier studies is that

columns can be designed to make very high-purity side-stream products, although a larger number of two-

product columns will frequently be more economical,except for certain ranges of feed composition and/orvolatilities (Glinos and Malone, 1985a). This is becausethe attainment of a high-purity side streammay requirelarge reflux ratios and a large number of stages,resulting in distillate or bottoms products that havemuch higher purities than required. Therefore, side-stream columns will often be advantageous when thereis not a high-purity requirement on the side stream orfor cases where the distillate or bottoms purity require-ments are quite high. However, if there is a sufficientdifference in boiling points between components, it canbe economical to achieve a side stream with a highpurity of the intermediate component.The geometric approach described in this paper does

address the feasibility question because intuition isoften lacking for nonideal mixtures. For nonidealmixtures, especially those that exhibit azeotropes, thereare no simple methods that can be used to design side-stream columns. A common approach is to use repeatedsimulation, e.g., by estimating the side-stream locationand flow rate, and then attempting to converge on asolution. Even when this approach is successful, it canbe a time-consuming method which gives little insight.For two-product columns, more efficient and robust

geometric design methods are available for both idealand nonideal mixtures. For example, a “boundary valuedesign procedure” (BVDP) for ternary mixtures was

* To whom correspondence should be addressed. Phone:413-545-0838. Fax: 413-545-1133. Email: [email protected].

† Parts of this work were presented at the AIChE AnnualMeeting, Miami Beach, FL, Nov 1995, Paper 189a.

Figure 1. Columns with a side stream above the feed or belowthe feed.

3653Ind. Eng. Chem. Res. 1996, 35, 3653-3664

S0888-5885(96)00036-X CCC: $12.00 © 1996 American Chemical Society

described by Levy et al. (1985). This approach can beused to calculate flows and the equipment sizes directlyfrom the product specifications for homogeneous mix-tures. Furthermore, it provides a representation ofinfeasible solutions so that some insight is availableeven when desired specifications cannot be met. Thesegeometric ideas have been generalized to provide mini-mum reflux (Julka and Doherty, 1990) and designmethods (Julka and Doherty, 1993) for mixtures withmore than three components.The purpose of this paper is to develop a geometric

method for the design of side-stream columns. Werestrict the model development here to mixtures con-taining three components. In the next section, wedevelop a model for single-feed side-stream columns.Next, the design procedure is outlined and some ex-amples are presented for both single- and double-feedcolumns. A procedure to calculate the minimum refluxfor side-stream columns is developed in the next section.Finally, we present several alternatives for the separa-tion of a four-component mixture in which side-streamcolumns can be used to reduce costs.

Model Development

The steady-state overall and component mass bal-ances for a two-product column are

and

The geometric interpretation of eqs 1 and 2 for ternarymixtures is simply the requirement that the feed andproduct compositions be collinear on a composition

diagram. For side-stream columns, the analogous massbalances are

which requires that the product compositions form atriangle with the feed composition as the “center ofmass”, as shown in Figure 2. Once the compositions ofthe product streams are known, it is possible to calculatethe (normalized) flows of all the product streams.The energy balance for an adiabatic column can be

written as

where h is the molar enthalpy, the subscripts V and Lindicate vapor and liquid, and t and b denote the topand bottom stages of the column. The feed quality q isthe dimensionless enthalpy of the feed, measured inlatent heat units relative to a saturated liquid; i.e., hf≡ (1 - q)λF, where λF is the heat of vaporization at thefeed composition. For constant molar flows and satu-rated liquid products, the energy balance (eq 5) takesthe simpler form

which can also be written as

in which r and s are the reflux and reboil ratios,respectively.We will consider cases where the feed composition,

temperature, and column pressure (and thus q) areknown. For the geometric design method, it is conve-nient to choose product compositions and a side-streamflow so that the mass balances in eqs 3 and 4 aresatisfied and then use eq 7 to relate s and r. It isstraightforward to relax the constant molar flow as-sumption, and it is used here only to illustrate theprinciples of the design method. We also take theproducts to be saturated liquids so that zD and zB inthe balances above will be replaced by xD and xB in mostof what follows. It is also easy and useful to consider avapor side stream, which we will do in some of the laterexamples.Along with the overall and component mass balances

and energy balances (eqs 3, 4, and 7), we requireexpressions for the stage-to-stage variations of composi-tions and, implicitly through the VLE, the boilingtemperatures. To preserve similarity with the two-product column, we use the conventional form for theoperating relationships in the rectifying (top) and strip-ping (bottom) sections as follows. For the rectifyingprofile, numbering down the column,

where g(xD) is the composition of the liquid in equilib-rium with a vapor of composition xD (g is the dew-point

Figure 2. Mass balance constraints for bottoms compositions ina side-stream column. The feed composition must occur insidethe triangle formed from the product compositions. The hatchedregion denotes the possible values of the bottoms composition whenthe distillate and side-stream compositions are fixed.

D + B ) F (1)

zDD + zBB ) zFF (2)

D + B + M ) F (3)

zDD + zBB + zMM ) zFF (4)

FhF ) [(VU)hVt - (LU)hL

t ] +

[(LL)hLb - (VL)hV

b] + MhM (5)

1 - q ) VU - VL (6)

1 - q ) (r + 1)D - sB (7)

yj+1r )

LU

VUxjr + D

VUxD j ) 1, ..., NU (8)

x1r ) g(xD)

3654 Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996

function). For the stripping profile, numbering up thecolumn,

where f(xB) is the composition of the vapor in equilib-rium with the liquid bottoms product (f is the bubble-point function).In the boundary value design procedure for simple

columns, the rectifying profile and the stripping profileare found beginning from initial conditions given by thedesired product compositions and then solving eqs 8 and9, respectively, along with the vapor-liquid equilibriumrelationships from one stage to the next within thecolumn until the final “pinch” or fixed point on eachprofile is reached. If the profiles intersect one another,the design is feasible and this geometric approach canbe developed to give both exact and approximate pro-cedures to find minimum reflux and designs. Formixtures with constant volatility, the results for mini-mum reflux are exactly equivalent to Underwood’smethod (Underwood, 1946, 1948), but the geometricapproach is more general because nonideal mixtures canalso be treated.For side-stream columns, however, we need a modi-

fied approach. It is well-known from studies of idealmixtures that there is a maximum side-stream purityof middle boiler that can be achieved without excessivecost (Glinos and Malone, 1988). (Actually, any purityof the side stream can be achieved in an ideal mixture,but high purities are often impractical because excessivestages and/or vapor boilup will be needed.) The gener-alization of a middle-boiling component in a nonidealmixture is any azeotrope or pure component whoseclassification is a saddle in the residue curve map.Thus, we expect that some saddles are feasible targetsfor the side-stream compositions. In mixtures withdistillation boundaries, the candidates are saddles inthe same distillation region as the distillate and bottomscompositions. Within a given region or for mixtureswithout distillation boundaries, the particular saddle-(s) that is a potential side-stream product(s) dependsupon the feed composition. (In the regions containingonly one saddle, the choice is unequivocal, but there aremany mixtures that have two saddles in the sameregion, and a decision is needed for these cases.) Wediscuss this point in more detail using the examplesbelow.We may attempt to place the side stream at any stage

on either the rectifying (upper side-stream) or stripping(lower side-stream) profiles. This sets the compositionof the side stream, xM, which is also the initial conditionfor the middle-section profile. It is convenient todescribe the profile in the middle section by one of twodifferent but equivalent forms of the mass balance,depending on the location of the side stream. Forexample, in a middle section, numbering down thecolumn, we can write

yj+1 )LM

VMxj + M

VMxM + D

VMxD j ) 1, ..., NM (10)

x1 ) xMand there is a similar expression for the calculation ofx if we number up the column.

Once we have chosen the side-stream location (andthereby its composition), we must also specify its flowin order to complete a design. Although it provides noguarantee that the desired compositions can be met, itis necessary that the side-stream flow and compositionmust at least satisfy the mass balances in eqs 3 and 4.For instance, for a column with the side stream abovethe feed (an “upper side-stream column”), if the feed hasbeen specified, the distillate composition, the side-stream location, and the overall mass balances demandthat the bottoms composition be placed in the shadedregion shown in Figure 2, perhaps at point B as shownin the figure. After we have selected all of the composi-tions, we can calculate the flows. A similar picture canbe developed for lower side-stream columns, where itis more “natural” to select the bottoms composition andthen seek bounds on the distillate composition.We must specify internal flows to calculate profiles

within the column, and it is also necessary to relate theflows in each of the sections to one another. We willrequire the following balances in the degree of freedomanalysis in the following section:

Degrees of Freedom and Specifications

For a single-feed, two-product column, there are 4degrees of freedom remaining after specifying thecolumn pressure, along with the flow rate, composition,and enthalpy of the feed (Fidkowski et al., 1991). Inthe BVDP, we usually choose to specify two purities inone product stream and a third purity in the otherproduct, along with either the reboil ratio or the refluxratio. With this information, the stage-to-stage com-position profiles can be found to determine if there is afeasible solution for the specified variables.For side-stream columns, there are independent

equations from the overall (eq 3, 1 equation) andcomponent (eq 4, c - 1 equations) mass balances, themass balances between column sections (eq 11, 4 equa-tions), and the overall energy balance (eq 6, 1 equation).In addition, a feasible column must have two profiles

(the middle and stripping profile for a side stream abovethe feed or the middle and rectifying profile for a sidestream below the feed) that have the same compositionat the feed stage (c - 1 equations). The remaining pairof profiles (rectifying and middle, or stripping andmiddle) will automatically have the same compositionat the side-stream stage (c - 1 equations). This is atotal of 3(c - 1) + 6 equations.The unknown variables are xM, xB, xD, NT, NB, NM,

D/F, M/F, B/F, LM/F, VM/F, VU/F, LU/F, VL/F, and LL/F.This is a total of 3(c - 1) + 12 variables, leaving 6degrees of freedom (DOF).It is convenient to specify some of the variables

involving the internal flows in terms of either the refluxratio, r ≡ LU/D, or the reboil ratio, s ≡ VL/B. For anupper side stream, we first choose xD and r (3 DOF),and this allows a calculation of the rectifying profile.Next, we choose a side-stream stage number, NT, on therectifying profile, and this 4th DOF determines xM. Thefinal 2 DOF can be specified by choice of either xB or

xj+1s )

VL

LLyjs + B

LLxB j ) 1, ..., NL (9)

y1s ) f(xB)

M ) LU - LM

VM ) VU

VU ) LU + D

LL ) VL + B (11)

Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996 3655

D/F and M/F; the value of xB must fulfill mass balanceconstraints, as shown in Figure 2. Alternatively, 1 molefraction in the bottoms product can be chosen, alongwith either the normalized distillate or side-stream flow.A similar analysis for the lower side-stream column

leads to a specification of xB and s, then NB, followedby either xD or B/F and M/F.

Design Procedure

The basic algorithm is similar for both the upper andlower side-stream columns, and we will describe onlythe case for an upper side-stream column (Table 1). Wewill specify the distillate and bottoms composition. Wewill also pick a side-stream location and the reflux ratioor reboil ratio, depending on whether the side streamis above or below the feed, respectively. Note that thefeed stage is at the intersection of the middle profileand the stripping profile.The choice of whether to specify a value of r or s

depends on the side-stream location. For instance, ifthe side stream is above the feed, then r is a naturalspecification since we calculate the rectifying profile inorder to choose the side-stream location. Alternatively,if the column has a lower side stream, it is more naturalto specify the reboil ratio. However, there are also caseswhere the side stream is located above the feed butwhere the reboil ratio is a more convenient specification.For example, if a pasteurization section is contemplatedin order to remove a small amount of light boilers fromthe mixture, while producing a main product that is themiddle boiler as the side stream, we may want tocompare the results to a two-product column doing theindirect split. An iterative procedure may be neededfor this case.

Feasibility

Side-stream columns have a larger range of feasibleproduct compositions than two-product columns. Theside-stream composition is limited to a subset of com-positions on the rectifying or stripping profiles, whichare approximately constrained by the singular pointsin the residue curve map at total reflux. This map is apicture of all the feasible solutions to

and is commonly used to display the limits imposed byphase equilibrium in nonideal mixtures. The solutionsof eq 12 are residue curves and analogues for columnprofiles at total reflux. The singular points of eq 12 arepure components and azeotropes, and a linear stability

analysis at these points can yield only three results: twonegative eigenvalues (a “stable node”sanalogous to ahigh boiler), two positive eigenvalues (an “unstablenode”sanalogous to a low boiler), or eigenvalues ofmixed sign (a “saddle”sanalogous to a middle boiler).The residue curve map for a constant volatility

mixture is shown in Figure 3. The residue curves beginat the lightest component and move toward the middle-boiling component before reaching the heaviest compo-nent. If we pick a residue curve close enough to thehypotenuse and near the lightest component, the curvewill pass close to the pure intermediate component andthis saddle is, thus, a target for the side-stream com-position.Since the rectifying profile has the same behavior as

the residue curve at high reflux, we can obtain a high-purity intermediate product, at the expense of theenergy required to provide a high vapor flow. Theenergy costs, the column diameter, and heat-exchangerareas scale with reflux (vapor rate). Consequently, sidestreams are not practical to provide high-purity inter-mediate products in many cases. Also, in order to obtaina side-stream target purity, we may need to overpurifythe distillate, i.e., begin a rectifying profile very closeto the hypotenuse.This geometric approach to feasibility can be extended

easily to nonideal mixtures and to mixtures with azeo-tropes and distillation boundaries. For mixtures withdistillation boundaries, such as acetone, isopropyl al-cohol, and water, there is more than one stable node(Figure 4). This mixture has two distillation regions;the upper region has the vertices at isopropyl alcohol(stable node), acetone (unstable node), and the isopropylalcohol-water azeotrope (saddle). The lower region hasvertices at water (stable node), acetone (unstable node),and the isopropyl alcohol-water azeotrope (saddle).Using the same logic as used for constant volatilitymixtures, we see that if the distillate is in either region,we may obtain a composition close to the binary azeo-trope as a side stream.

Designs for Single-Feed Columns

Ideal Systems. The simplest vapor-liquid modelused in distillation is the constant volatility model. As

Table 1. Design Algorithm for an Upper Side-StreamColumn

1. Specify the column pressure, feed rate (F),feed composition (zF), and enthalpy (q)

2. Choose the distillate composition, xD (2 DOF)3. Choose a reflux ratio, r (1 DOF)4. Solve for the rectifying profile (eq 8 and VLE)5. Choose a side-stream location (NT) on the rectifyingprofile (1 DOF)

6. Choose the bottoms composition, xB (2 DOF)7. Solve for the flows of the distillate, bottoms,and side stream (eqs 3, 4)

8. Solve for the middle profile (eq 10 and VLE)9. Solve for the stripping profile (eq 9 and VLE)10. If intersection of middle and stripping profiles, stop.Otherwise, go to 11.

11. Adjust r or another specification, and repeat from step 2.

dxdê

) x - y(x) (12)

Figure 3. Residue curve map for R13 ) 9, R23 ) 2.


discussed above, it is possible to obtain nearly purecomponents in each product with sufficient energy andstages. Whether it is economical to do this or notdepends on the feed and product compositions and therelative volatilities.The residue curve map for this mixture (Figure 3)

shows two nodes and one saddle, where the relativevolatilities are R13 ) 9 and R23 ) 2. The feed composi-tion is balanced (zF ) 0.3, 0.3, 0.4). We can split thismixture into nearly pure products (99% pure) using 2columns in the direct sequence with 28 stages in thefirst column and 24 stages in the second column. Wechoose to design the columns at a reflux ratio 40% abovethe minimum reflux, although this could also be opti-mized.We need criteria for evaluating the costs of each

column for comparison of alternatives to this simple

sequence. However, a detailed economic analysis canbe time-consuming, yet still uncertain, and a simplermethod is often adequate for conceptual design. Forexample, it has been demonstrated that the total vaporrate is a good indicator for comparing designs (Glinosand Malone, 1985b) provided that the vapor boilup forall the streams can be provided with utilities at a similarcost.The total vapor rate per mole of feed for the direct

sequence in this example is ∑V/F ) 1.8, and 53theoretical stages are required. We can compare thiswith the side-stream column (Figure 5), where the sameproduct purities are achieved at a much larger value ofV/F ) 9.23, although with 36 stages. While the numberof stages is lower for the side-stream column, the columndiameter is larger than for the first column in the directsequence, due to the large vapor flow rate. In addition,the reboiler will be larger and the operating costs willbe much larger for the side-stream column. For thisparticular case, a side-stream column is not likely tobe cost-effective.If the relative volatility of the lightest component is

larger, and if the lightest component is present only insmall amounts, the results can be quite different. Forinstance, consider the case of R13 ) 18, R23 ) 3, and afeed composition (zF ) 0.05, 0.45, 0.5). The directsequence has ∑V/F ) 1.3 and a total of 41 stages forthe specification of 99% purity of the key component ineach product stream. We find ∑V/F ) 2.0 and a totalof 33 stages, for the indirect sequence.The side-stream column has a total of 33 stages,

which compares favorably to the direct sequence. Sincewe have specified a high-purity product, we have a highreflux ratio of 22 (on account of a small distillate flowrate), even though the relative volatility for the lightestcomponent is high. Although the reflux ratio is high,the reflux flow is not so large and the vapor rate forthe side-stream column, V/F ) 1.1, is lower than eitherthe direct or indirect sequences. The side-stream

Figure 4. Residue curve map for acetone, isopropyl alcohol, andwater.

Figure 5. Liquid composition profile for separation of a constant relative volatility mixture (R13 ) 9, R23 ) 2) using a side-stream column.The open circles form the stripping profile, the filled squares form the middle profile, and the open diamonds form the rectifying profile.


column will be cheaper since there is a single shellinstead of two and two heat exchangers instead of four.

Nonideal Mixtures

An isopropyl alcohol, acetone, and water mixture isproduced in the manufacture of acetone from isopropylalcohol using an azeotropic feed of isopropyl alcohol andwater. The vapor-liquid equilibrium for this mixturecan be described by the Wilson model (Gnehling et al.,1978, 1981, 1988). There is a low-boiling azeotropebetween isopropyl alcohol and water, and the residuecurve map (Figure 4) shows a distillation boundary fromthe azeotrope to pure acetone.The feed composition to the reactor is near the

isopropyl alcohol/water azetrope. The resulting com-position of the reactor exit stream is in the lowerdistillation region and is fed to the separation system.With this feed, a direct sequence (Figure 6) can producenearly pure acetone, nearly pure water, and a productwith a composition near the azeotrope for recycle to thereactor. This sequence has a total of 40 stages and ∑V/F

) 2.7. The results for the first column in the sequenceare summarized in Table 2. A side-stream column(Figure 7) with a vapor side stream can yield betterresults than the direct sequence for this feed. It has40 stages and a nearly identical vapor flow rate V/F )2.6 and is an attractive alternative that can be used toreplace the two columns of the direct sequence.A different case arises for this same mixture if the

feed composition contains a small amount of water (e.g.,zF ) 0.4, 0.55, and 0.05, the mole fractions being in orderof acetone, isopropyl alcohol, and water) and we wishto recover pure acetone and isopropyl alcohol for whicha direct split would be feasible. This sequence has atotal of 63 stages and ∑V/F ) 5.9. The second columnin the sequence has a bottoms product of isopropylalcohol and a distillate near the azeotrope. Alterna-tively, a side stream (Figure 8) near the azeotropecomposition allows us to obtain pure isopropyl alcoholand pure acetone as bottoms and distillate products,respectively, from a single column. The total numberof stages is 52, and the vapor flow rate V/F ) 5.0. This

Figure 6. Direct sequence and liquid composition profiles for the first column to obtain pure acetone. Note that the column profile inthe triangle corresponds to the first column in the sequence. The open circles form the stripping liquid profile, and the open diamondsform the rectifying profile.

Table 2. Summary of Design Specifications and Resultsa

Figure 5 Figure 6 Figure 7 Figure 8

reflux ratio 3.0 3.0 2.874 10.86z1,F 0.3 0.63 0.63 0.4z2,F 0.3 0.07 0.07 0.55z3,F 0.4 0.3 0.3 0.05x1,D 0.99 0.99 0.99 0.9933x2,D 0.01 0.0001 0.0001 0.0007x3,D 1.0 × 10-10 0.0099 0.0099 0.006x1,B 1.0 × 10-10 1.0 × 10-5 1.0 × 10-10 1.0 × 10-20

x2,B 0.01 0.1923 0.01 1.0x3,B 0.99 0.8077 0.999 1.0 × 10-5

x1,M or y1,M 0.0094 n/a 0.0009 0.0004x2,M or y2,M 0.9905 n/a 0.6539 0.761x3,M or y3,M 2.014 × 10-5 n/a 0.3452 0.2386total stages 36 33 40 52side-stream stage 26 n/a 8 30q 1.0 1.0 1.0 1.0V/F 9.307 2.545 2.572 4.974

a The specifications appear in italics. Note that the mole fractions are in order of increasing boiling points for the components theyrepresent.


alternative has fewer total stages, a lower vapor rate,fewer columns, and fewer heat exchangers than thedirect sequence, and therefore, it will be less expensive.As stated above, this technique can be used without

the assumption of constant molar flows. The results ofa profile calculation including an energy balance andenthalpy changes were compared to a simulation donewith HYSYS software, version 1.0. The results are ingood agreement, as shown in Table 3.The savings for a side-stream column over the direct

sequence is very sensitive to the side-stream composi-

tion specification. As the purity of the side streamapproaches the binary isopropyl alcohol-water azeo-trope (72 mol % isopropyl alcohol), the vapor flowincreases in the side-stream column (Figure 9). This isdue to the need to overpurify the bottoms product inorder to reach a profile that approaches the azeotropiccomposition in the side stream. If the mole fraction ofisopropyl alcohol in side-stream composition is in-creased, V/F decreases, and the number of stagesincreases as this composition is approached. The sav-ings in stages and V/F as a function of the side-stream

Figure 7. Side-stream column and liquid composition profile for the production of acetone. The open circles form the stripping profile,the filled squares form the middle profile, and the open diamonds form the rectifying profile.

Figure 8. Side-stream column liquid composition profile to obtain pure acetone and isopropyl alcohol. The open circles form the strippingprofile, the filled squares form the middle profile, and the open diamonds form the rectifying profile.


composition is shown in Figure 10. For an equalnumber of stages (81 mol % isopropyl alcohol in the sidestream or distillate), the savings in the vapor rate arenearly 80% for the side-stream column. The ideal side-stream composition is actually an optimization problemwhich should include the reactor design and energycosts.

Minimum Reflux

Minimum reflux calculations for single-feed, two-product columns can be performed using geometricmethods and with a numerical solution via continuationmethods (Fidkowski et al., 1991). These methods applyto both sharp and nonsharp splits, where at least onecomponent is being removed in each exit stream, andinvolve tracking the fixed points of certain profileequations. For instance, the fixed points (pinches) of

the rectifying equation (eq 8) can be found by solving

and for the stripping section

Side-stream columns exhibit minimum reflux geom-etries similar to simple columns (Kohler et al., 1994).The minimum reflux ratio is governed by one profilepinching on another, and to a close approximation,pinches are aligned with the feed composition. The

Table 3. Comparison of Non-CMO Profiles and a Simulationa

side stream direct

design simulation design simulation

reflux ratio 13.61 13.61 11.39 11.39reboil ratio 11.5 11.559 6.16 6.121distillate rate 0.4026 0.4026 0.403 0.403bottoms rate 0.394 0.394 0.597 0.597z1,F 0.4 0.4 0.4 0.4z2,F 0.55 0.55 0.55 0.55z3,F 0.05 0.05 0.05 0.05x1,D 0.9933 0.994 0.9933 0.994x2,D 7.0 × 10-4 6.323 × 10-4 7.0 × 10-4 7.211 × 10-4

x3,D 0.006 0.006 0.006 0.006x1,B 1.0 × 10-20 1.218 × 10-21 1.0 × 10-9 1.865 × 10-11

x2,B 1.0 1.0 0.9203 0.920x3,B 1.0 × 10-5 2.365 × 10-5 0.0797 0.08y1,M 3.0 × 10-4 4.247 × 10-5 n/a n/ay2,M 0.7655 0.765 n/a n/ay3,M 0.2341 0.235 n/a n/atotal stages 53 53 36 36feed stage 42 42 25 25side-stream stage 30 30 n/a n/aq 1.0 1.0 1.0 1.0V/F 4.533 4.6 3.679 3.7

a The distillate and bottoms rate are normalized by the feed rate. The specifications appear in italics. Note that only the results of thefirst column in the direct sequence are shown. The binary separation shows similar agreement.

Figure 9. Comparison of the side-stream column to the directsequence over a range of compositions in the side stream anddistillate in the second column of the direct sequence, respectively.

Figure 10. Comparison of the savings of the side-stream columnvs the direct sequence over a range of compositions. The composi-tions are for the side stream and the distillate in the second columnof the direct sequence.

y(x̂r) -LU

VUx̂r - D

VUxD ) 0 (13)

x̂s -VL

LLy(x̂s) - B

LLxB ) 0 (14)


strategy for solving for the minimum reflux does differ,though, since there is a new section of the column. Themiddle-profile pinch equation is

The key to calculating the minimum reflux ratio forside-stream columns is to know which pinches to align.We need to know when the profiles will exhibit the“direct” or “indirect” geometries (Figure 11a or b). Inorder to calculate the minimum reflux for feed andproduct specifications that follow direct geometry, thestripping node pinch, the feed composition, and therectifying saddle must be aligned (Figure 11a). Simi-larly, for the indirect geometry, the middle-section nodepinch, the feed composition, and the stripping saddlepinch must all be aligned (Figure 11b). For most cases,there are two notable results. For a column with a sidestream above the feed, if the bottoms composition isclose to the heavy boiling component or azeotrope, aindirect geometry will normally result. Alternatively,for a column with a side stream below the feed, if thedistillate composition is close to the light boiling com-ponent or azeotrope, a direct geometry will normallyresult.An important similarity for both the two-product

column and the side-stream column is that two of theprofiles pinch at the feed tray (stripping and rectifying,stripping and middle, or rectifying and middle, depend-ing on which geometry controls).Figure 11c shows the “transition” geometry for a

upper side-stream column. The line that divides distil-late and bottom compositions leading to the direct andindirect geometries is the “transition line”. This issimilar to the results of Fidkowski et al. 1993) (Figure3c) for simple columns. The difference is that the feed,distillate, and bottoms compositions are not collinear,due to the presence of the side stream.If we examine an upper side-stream column at

minimum reflux for the transition split, both the middleand stripping profiles pinch at the same point. For thespecial case of a saturated liquid feed, these pinches willoccur at the feed composition xF.The stripping profile depends only on the bottoms

composition and the reboil ratio, and for a given bottomscomposition, there will be only one reboil ratio that leadsto the stripping section pinching at the feed composition.This does not depend on what is happening in the uppercolumn section(s) (i.e., whether or not there is a sidestream above the feed). Therefore, the transition linefor side-stream columns is identical to the one for simplecolumns with the following interpretation. The transi-tion line connects the bottom composition, the feedcomposition, and the average composition of the productstreams above the feed (i.e., distillate and side stream)for a side stream above the feed. A similar result isreached for a side stream below the feed. The transitionline can be found by computing the solutions to theequation

With this solution, we can then delineate which splitsare direct and indirect. This allows the correct criteriato be applied when calculating the minimum refluxratio.

In solving for the minimum reflux for a side-streamcolumn, we must perform the following steps:1. Find the transition line by solving eq 16 with xf

and yf related by VLE.2. If the bottoms composition indicates a direct

geometry, use the rectifying saddle, the middle-section

y(x̂) -LM

VMx̂ - M

VMxM - D

VMxD ) 0 (15)

qxf + (1 - q)yf - zF ) 0 (16)

Figure 11. Upper side-stream column profiles for (a) directgeometry, where the stripping profile pinches on the middle profile;(b) indirect geometry, where the middle profile pinches on thestripping profile; and (c) transition geometry, where the middleprofile and the stripping profile pinch at the same point. Thetransition line is denoted by the dashed line.


node, and the feed composition to determine the fixed-point “volume” (Fidkowski et al., 1991).3. If the bottoms composition corresponds to indirect

geometry, use the stripping saddle, the middle-sectionnode, and the feed composition to determine the fixed-point “volume”.4. The minimum reflux corresponds to a “volume” of

zero. A turning point in the volume-reflux graphcorresponds to a tangent pinch and is treated the sameway as in Fidkowski et al. (1991).

Double-Feed Columns

The design method for single-feed columns with sidestreams naturally extends to double-feed columns. Asan example, we return to the acetone, isopropyl alcohol,and water system and consider two feeds in the lowerdistillation region. The lower feed is rich in water (20%acetone, 20% isopropyl alcohol, 60% water), and theupper stream is rich in acetone (80% acetone, 10%isopropyl alcohol, 10% water). We have selected 99%purity of acetone in the acetone product stream, 99%

purity of isopropyl alcohol in the isopropyl alcoholproduct stream, and 99% water in the water productstream.The direct sequence has a distillate product from the

first column rich in acetone. The bottoms productcontains primarily isopropyl alcohol and water and issent to the second column, where it is split into adistillate with a composition near the azeotrope and abottoms containing primarily water. The total vaporflow rate (V/(FL + FU)) for this sequence is 2.33, andthe total number of stages is 39. The side-streamcolumn has a bottoms product of water, a distillate ofacetone, and a side stream near the azeotrope composi-tion. The vapor flow for this column is 2.29, and thetotal number of stages is 33. Again, because this columncan replace a sequence of two columns and has fewerstages, roughly the same vapor flow rate, fewer heatexchangers, and less instrumentation, it will be moreeconomical.

Four-Component Example

The ideas presented in this paper can be used togenerate process alternatives. Consider a four-compo-nent mixture of acetaldehyde, methanol, ethanol, andwater with the residue curve map structure shown inFigure 12. This mixture has three azeotropes, all onthe acetaldehyde, ethanol, and water face. There is adistillation boundary that separates the tetrahedroninto two regions, one rich in water, the other lean inwater as shown in the figure. This mixture wasdiscussed in a previous paper (Julka and Doherty, 1993)and the original data appear in d’AÄ vila and Silva (1970).For feed mixtures with a composition on the water-

rich side of the distillation boundary, we can perform adirect split in the first column, where acetaldehyde isthe distillate and the bottoms product is on the methanol/ethanol/water face. Still more alternatives may bepossible, such as the indirect split, where water is takenout as the bottoms product; that and some of the otheralternatives involve crossing distillation boundaries.The first sequence (Figure 13) has five columns. The

first column removes nearly all of the acetaldehyde inthe distillate, leaving the remaining three componentsin the bottoms stream. The second column removesnearly all of the methanol in the distillate and sendsthe bottoms product of ethanol and water to a “precon-

Figure 12. Residue curve map structure of acetaldehyde, metha-nol, ethanol, and water at 1 atm of pressure. Note that there isa distillation boundary denoted by the hatched region.

Figure 13. First sequence to separate acetaldehyde, methanol, ethanol, and water. This sequence has a total of 5 columns, 10 heatexchangers, 178 stages, and a normalized vapor flow of 12.19.


centrator” column. This third column concentrates thedistillate to a composition near the ethanol/water azeo-trope and removes water in the bottoms. The last twocolumns are an extractive distillation sequence to breakthe azeotrope using ethylene glycol as an extractiveagent.The second sequence (Figure 14) consolidates the

second and third columns. A side-stream column canbe used to remove methanol as a distillate, water as abottoms product, and a side-stream product near theethanol-water azeotrope. The need for a separatepreconcentrator column has been eliminated, and theside stream is fed directly to the extractive distillationsequence. The total number of stages needed is thesame, but the total vapor flow is reduced by ap-proximately 20% compared to the first alternative.The third sequence (Figure 15) introduces a new

extractive distillation configuration. Ethylene glycolhas a high volatility relative to with water, which makesthat binary mixture easy to separate. If a side-streamvapor is used to recover the water, the entrainerrecovery column can be eliminated since the entraineris in the bottom stream. The water purity in the sidestream is 99%, and this is sent to treatment along withthe water from the second column. This sequence hasthree columns, fewer stages, and a lower total vaporflow rate.The three sequences shown above are summarized in

Table 4. All of these sequences have identical designsfor the first column. The process alternatives lie inusing side streams to replace various downstreamcolumns.

Conclusions

This paper has described a method to design side-stream columns. The methods apply to ideal mixturesas well as to mixtures with azeotropes and distillationboundaries. Middle-boiling components and saddleazeotropes are potential side-stream products.Side-stream columns can be economical under certain

process conditions and design requirements. Some ofthe criteria which favor the use of side-stream columnsare as follows:1. There is an imbalanced feed, such as very little of

a middle-boiling component.2. The sidestream can be taken with flexible purity

requirements, such as side streams going to wastetreatment, recycle, and as azeotropic feeds to othercolumns. The best composition of the side streamshould then be computed through a optimization overthe entire system. Such an optimization could be animportant application of the methods displayed here.An additional advantage of a side stream is that it

provides an exit point for middle-boiling trace compo-nents.For some designs, side-stream columns can lead to

lower capital and operating costs. The inclusion of side-stream designs expands the tools available so that bettersystems can be achieved.

Acknowledgment

We are grateful for financial support provided by theUniversity of Massachusetts Center for Process Designand Control. We also thank Hyprotech for use of thesimulator software HYSYS.

Nomenclature

c ) number of pure components in the mixtureB ) bottoms flow rateD ) distillate flow rateF ) flow of overall feedf(x) ) vapor composition at the bubble point of a liquidwith composition x

g(y) ) liquid composition at the dew point of a vapor withcomposition y

h ) molar enthalpyL ) liquid stream or flow rateM ) side-stream flow rateN ) number of stagesP ) column pressureq ) dimensionless enthalpy of the feed (feed quality)r ) reflux ratios ) reboil ratioV ) vapor stream or vapor flow ratex ) vector of liquid mole fractionsy ) vector of vapor mole fractionsz ) vector of mole fractions

Greek Symbols

Rij ) relative volatility of component i with respect tocomponent j

Figure 14. Second sequence to separate acetaldehyde, methanol,ethanol, and water. This sequence has a total of 4 columns, 8 heatexchangers, 178 stages, and a normalized vapor flow of 10.12.

Figure 15. Third sequence to separate acetaldehyde, methanol,ethanol, and water. This sequence has a total of 3 columns, 6 heatexchangers, 166 stages, and a normalized vapor flow of 9.84.

Table 4. Summary of Design Results for theFour-Component Separation Sequences

sequence

first second third

stages 178 178 166shells 5 4 3heat exchangers 10 8 6vapor flows ∑V/F0 12.19 10.12 9.84


λF ) latent heat of vaporization of the feedê ) warped time

Superscripts

ˆ ) fixed pointb ) bottom trayf ) feed trayr ) rectifying sections ) stripping sectiont ) top tray

Subscripts

B ) bottomsD ) distillateF ) feedL ) lower section of columnM ) middle section of columnU ) upper section of column

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Received for review January 26, 1996Revised manuscript received July 8, 1996

Accepted July 9, 1996X

IE960036T

X Abstract published in Advance ACS Abstracts, October 1,1996.


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A Geometric Design Method for Side-Stream Distillation Columns †